Szentendre (St. Andrew) is a little pretty town near Budapest, so it must be a complete daytrip town from Budapest. When you go out of the train, head north, walk under the subway. And then, taking Kossuth Lajos utca, and then you will reach Fo ter, the center of town. Around this square there some nice galleries, and old churches, like Blagovestenska Templom. And, then you can climb the castle hill. On the top you will find Belgradi Szekesegyhaz (Belgrade Chathedral). In the surburbe there is Szabadteri Neprajzi Museum (Open Air Ehonographic Museum). To walk around this museum is very plesant. There are many gift shops here. So, it must be a good town for buy folk arts.
Directions: 20 kms north of Budapest, along highway #12; take Szentendre HEV trains in direction Szentendre from Batthyany ter M2 station. The travel takes about 45 minutes. This train passes Aquincum, too.
Website: http://www.szentendre.hu